Details

sample25.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.1b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

29646×	`*-un-lft-identity`
17776×	`distribute-lft-out`
11948×	`times-frac`
4332×	`associate-l`
2250×	`add-sqr-sqrt` `add-cube-cbrt`
588×	`associate-/l*`
168×	`associate-/r/`
138×	`associate-/l/`
88×	`flip3-+` `flip-+`
84×	`div-inv`
43×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
7×	`fma-def`
6×	`associate-+l+` `frac-2neg` `clear-num` `sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`+-commutative`

Counts

4 → 4741

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
47.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
192.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
24.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
148.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
156.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

4753 → 4753

Iterations

Useful iterations: 1 (69.0ms)

Iter	Nodes	Cost
0	1610	115382
1	5001	107229

prune1.3s

Filtered

4753 candidates to 330 candidates (6.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	4746	7	4753
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	4747	8	4755

Merged error: 0.6b

Counts

4755 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

38406×	`*-un-lft-identity`
16768×	`times-frac`
16427×	`distribute-lft-out`
11981×	`add-sqr-sqrt`
9994×	`associate-/l*`
7040×	`frac-times`
5839×	`add-cube-cbrt`
5766×	`associate-l`
4892×	`distribute-lft-out--`
2943×	`associate-/r*`
2444×	`difference-of-squares`
2438×	`associate-/l/`
1230×	`unswap-sqr`
397×	`clear-num`
396×	`frac-2neg`
352×	`flip3--` `flip--`
339×	`div-inv`
320×	`associate-*l/`
78×	`associate-r`
64×	`associate-/r/`
52×	`add-exp-log` `add-cbrt-cube`
27×	`flip3-+` `flip-+`
26×	`cbrt-undiv` `div-exp`
22×	`associate-*r/`
8×	`prod-exp` `cbrt-unprod`
6×	`pow1` `un-div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 9762

Calls

4 calls:

906.0ms	(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
32.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
85.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
124.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
158.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify3.5s

Algorithm

egg-herbie

Counts

9774 → 9774

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5003	317175

prune8.5s

Filtered

9774 candidates to 1870 candidates (19.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	9770	4	9774
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	9774	8	9782

Merged error: 0.6b

Counts

9782 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite33.7s

Algorithm

rewrite-expression-head

Rules

413003×	`*-un-lft-identity`
244349×	`distribute-lft-out`
134825×	`times-frac`
86529×	`associate-/l*`
62621×	`associate-l`
58972×	`sqrt-div`
50232×	`frac-times`
48867×	`sqrt-prod`
32817×	`add-sqr-sqrt`
32734×	`add-cube-cbrt`
22754×	`associate-/l/`
9740×	`associate-/r*`
3550×	`associate-r`
3066×	`associate-/r/`
2176×	`flip3-+` `flip-+`
1533×	`div-inv`
1379×	`clear-num`
1378×	`frac-2neg`
546×	`associate-*r/`
92×	`associate-*l/`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `un-div-inv` `cbrt-unprod`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 59181

Calls

4 calls:

16.9s	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
199.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
26.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
123.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.4s	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
85.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify27.1s

Algorithm

egg-herbie

Counts

59193 → 59193

Iterations

Useful iterations: 0 (334.0ms)

Iter	Nodes	Cost
0	5428	2639078

prune17.6s

Filtered

59193 candidates to 3334 candidates (5.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	59191	2	59193
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	59193	8	59201

Merged error: 0.6b

Counts

59201 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.9b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

3715×	`*-un-lft-identity`
2144×	`distribute-lft-out`
1408×	`times-frac`
548×	`associate-l`
546×	`sqrt-prod`
375×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`associate-/r*`
45×	`associate-/r/`
34×	`associate-/l*`
20×	`sqrt-div`
17×	`add-exp-log`
15×	`flip3-+` `add-cbrt-cube` `flip-+`
12×	`div-inv`
8×	`associate-/l/`
7×	`div-exp`
6×	`pow1` `cbrt-undiv`
5×	`frac-2neg` `clear-num`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 1006

Calls

4 calls:

12.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
56.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
28.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
222.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
85.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify298.0ms

Algorithm

egg-herbie

Counts

1018 → 1018

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	974	17929
1	4805	15112
2	5001	15112

prune976.0ms

Filtered

1018 candidates to 192 candidates (18.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1017	1	1018
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	1019	7	1026

Merged error: 0.6b

Counts

1026 → 7

regimes82.0ms

Accuracy

61.2% (0.9b remaining)

Error of 2.1b against oracle of 1.2b and baseline of 3.6b

bsearch75.0ms

Steps

Iters	Range		Point
10	2.991850971092621e+153	5.703672081453638e+164	3.0069364258348726e+164

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms

sample555.0ms

Algorithm

intervals

Results

310.0ms	8000×	body	80	valid
97.0ms	8000×	pre	80	true